Question

The weight of an object at earth's surface is $700gwt$. What will be its weight at the surface of a planet whose radius is $1/2$ and mass is $1/7$ of that of the earth ?

• A. 200 g wt.
• B. 400 g wt.
• C. 50 g wt.
• D. 300 g wt.

Answer 1

Answer: (B)

Weight at earth's surface $w=mg$
Acceleration due to gravity at earth's surface
$g=\frac{G{M}_c}{R_e^2}$
For planet, $g^{\prime }=\frac{GM}{R^2}=\frac{G{M}_c/7}{{\left(R_e/2\right)}^2}$
$=\frac{4}{7}\frac{G{m}_e}{R_e^2}=\frac{4}{7}g$
$\therefore$ Weight at the surface of planet $=m{g}^{\prime }$
$=m\left(\frac{4g}{7}\right)$
$=\frac{4}{7}mg=\frac{4}{7}\times 700$
$=400gwt$